On Wednesday, at least three Palestinians were killed after Israeli forces launched a series of air raids which it said were a response to Palestinian attacks.
Binyamin Netanyahu, the Israeli prime minister, told his weekly cabinet meeting on Sunday that 20 mortar bombs and rockets had been fired at Israel in the last week.
"I view this very seriously," he said.
"The government's policy is clear, any shooting at our territory will receive an immediate and powerful response."
Rocket and mortar attacks were also cited as the reason for Israel's 22-day offensive against Hamas in the Gaza Strip, which began in late December 2008 and left more than 1,300 Palestinians dead.
Thirteen Israelis were killed during the conflict.